Mijailo Mijailovic, 27, is serving a life sentence in a maximum security jail in Kumla, west of Stockholm.
He stabbed Lindh repeatedly as she shopped at a department store in the capital in September 2003 and was sentenced the following year.
In September 2005, exactly two years after the bloody attack, Mijailovic spent one month at a psychiatric unit in the northern Swedish town of Sundsvall after his mental health deteriorated.
While there, he attacked a patient with a piece of metal from a radiator. The patient sustained multiple wounds to the head and had to have a fingertip amputated, the online edition of local daily Sundsvalls Tidning said.
Mijailovic has pleaded guilty to the attack through his lawyer, the paper said.
The country was sent into a state of shock in 2003 after the murder of Lindh, who was tipped to one day become prime minister.
Mijailovic, who had a history of mental problems, claimed during his three trials that he heard “voices” telling him to attack Lindh. However he insisted he did not mean to kill her and had no motive.